Nonlinear fractional stochastic PDEs and BDSDEs with Hurst parameter in (1/2,1)

Abstract

We study a class of semilinear stochastic partial differential equations driven by a fractional Brownian motion with Hurst parameter H∈(1/2,1). For this end, we use the doubly stochastic interpretation through a backward doubly stochastic differential equations, driven by both a standard and an independent fractional Brownian motion. The Doss–Sussmann transformation is employed to establish the link between the backward doubly stochastic differential equation and a backward stochastic differential equation, driven only by the standard Brownian motion, through which the stochastic viscosity solution of the stochastic partial differential equation is studied.